The temperature coefficient of resistivity of iron is 5.0 x 10-3 /oC; that of carbon is -0.50 x 10-3 /oC. When an iron wire and a carbon rod, each having the same 10 resistance at 20 oC, are cooled from that temperature to -80 oC, the new ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature is

1. -0.10.

2.+;2.1.

3. -10.

4. +;1.9.

5.+;10.

2.   + 2.1

Explanation:

Formula for resistance is as follows

R_t = R₀ ( 1 + α t )

R_t is resistance at changed temperature , Ro is resistance at initial temperature , α is temperature coefficient of resistivity . t is temperature change .

For iron , R₀ = 10 , α = 5 x 10⁻³ , t = - 100 degree

R_t = 10( 1 + 5 x 10⁻³ x - 100 )

= 10( 1 - 5 x 10⁻³ x  100 )

10 x ( 1 - .5 )

10 x .5

For carbon

, R₀ = 10 , α = - 0.5 x 10⁻³ , t = - 100 degree

R_t = 10( 1 - 0. 5 x 10⁻³ x - 100 )

= 10( 1 +  .5 x 10⁻³ x  100 )

10 x ( 1 + .05 )

10 x 1.05

Required ratio

= 10 x 1.05 / 10 x .5

= 105 / 50

= 21 / 10

= 2.1

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